The uniqueness condition for the Ising model is given by \(\beta \in \left(\frac{\Delta -2}{\Delta },\frac{\Delta }{\Delta -2}\right)\) ,
where \(\Delta =\Delta _G\ge 3\)  is the maximum degree of \(G\) .
When \(\beta > \frac{\Delta }{\Delta -2}\)  or \(\beta <\frac{\Delta -2}{\Delta }\) , either the single-site dynamics is slow mixing or the sampling problem itself is intractable [1]}, [2]}.
